When does this inequality have a finite number of integer solutions?

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Let \(a\), \(b\), \(c\) be positive numbers. There are finitely many positive whole numbers \(x\), \(y\) which satisfy the inequality \[a^x > cb^y\] if

1. \(a>1\) or \(b<1\).

2. \(a<1\) or \(b<1\).

3. \(a<1\) and \(b<1\).

4. \(a<1\) and \(b>1\).

It’s important to notice that the question refers to a finite number of solutions…

Can we use logarithms to rewrite the inequality?